Solve 21n^3-3n^2-35n+5

$$21 n ^ { 3 } - 3 n ^ { 2 } - 35 n + 5$$

Factor

$$\left(7n-1\right)\left(3n^{2}-5\right)$$

Solution Steps

Do the grouping 21n^{3}-3n^{2}-35n+5=\left(21n^{3}-3n^{2}\right)+\left(-35n+5\right), and factor out 3n^{2} in the first and -5 in the second group.

$$3n^{2}\left(7n-1\right)-5\left(7n-1\right)$$

Factor out common term 7n-1 by using distributive property. Polynomial 3n^{2}-5 is not factored since it does not have any rational roots.

$$\left(7n-1\right)\left(3n^{2}-5\right)$$

Evaluate

$$\left(7n-1\right)\left(3n^{2}-5\right)$$